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Looking at gradients and values for x and y for straight-line graphs

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In a straight-line graph the general equation is $y = mx + c$ where c is the intercept and m is the gradient.

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$y = \\var{a}x + \\var{b}$

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$\\var{a}$

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$\\var{b}$

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$x$

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$y$

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Identify the gradient in the following straight-line graph equation:

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Identifying the gradient from a straight-line graph equation y=mx+c

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In a straight-line graph the general equation is $y = mx + c$ where c is the intercept and m is the gradient.

", "rulesets": {}, "parts": [{"prompt": "

$y = \\var{a}x + \\var{b}$

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$\\var{a}$

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$y$

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$x$

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Identify the intercept in the following straight-line equation:

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Identifying the intercept from a y=mx+c equation

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Calculating gradient", "extensions": [], "custom_part_types": [], "resources": [["question-resources/dydx.png", "/srv/numbas/media/question-resources/dydx.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}], "functions": {}, "ungrouped_variables": ["dy", "dx", "grad"], "tags": [], "advice": "

Gradient is calculated as:

\n

$\\frac{\\text{difference in }y}{\\text{difference in }x}$

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If the difference of $y = \\var{dy}$, and the difference in $x = \\var{dx}$, calculate the gradient.

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A student is trying to find the gradient on the graph below.

\n

{image('resources/question-resources/dydx.png')}

\n

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Calculating gradients

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When calculating y with a given value of x, take the equation of the line (y = mx + c) and input the value of x.

\n

For example, for y = 2x + 3, if x = 5:
y = 2(5) + 3
y = 10 + 3
y = 13

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What is $y$ if $x = \\var{x1}$?

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What is $y$ if $x = \\var{x2}$?

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What is $y$ if $x = \\var{x3}$?

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What is $y$ if $x = \\var{x4}$?

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What is $y$ if $x = \\var{x5}$?

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For the straight line graph $y = \\var{m}x + \\var{c}$:

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Completing a table of x and y values from a straight line graph equation.

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Input your value of x into the equation given.

\n

E.g., for the equation $y = \\var{m}x + \\var{c}$ and  $x = \\var{x1}$:
$y = (\\var{m}$ x $\\var{x1}) + \\var{c}$

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$x = \\var{x1}$

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$x = \\var{x2}$

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$x = \\var{x3}$

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$x = \\var{x4}$

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For the line $y = \\var{m}x + \\var{c}$, what is y if:

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Finding x and y values for straight line graphs

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