In y=mx+c, what does c represent?

The y-intercept, where the line crosses the y-axis.

What does a negative gradient look like?

A line sloping downwards from left to right.

How do you find the equation of a line through two points?

Find m, substitute one point into y=mx+c, and solve for c.

How do you check if a point lies on a line?

Substitute its x-value and see if you get its y-value.

What does the gradient mean in a real-life graph?

The rate of change, e.g. litres per minute.

Linear functions and graphsIB MYP Maths Standard: Flashcards

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What is the equation of a straight line in gradient-intercept form?

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What is the equation of a straight line in gradient-intercept form?: $y=mx+c$
In $y=mx+c$ , what does $m$ represent?: The gradient (steepness).
In $y=mx+c$ , what does $c$ represent?: The $y$ -intercept, where the line crosses the $y$ -axis.
What is the gradient formula?: $m=\frac{y_2-y_1}{x_2-x_1}$
Gradient between $(1,3)$ and $(5,11)$ ?: $\frac{11-3}{5-1}=2$
What does a negative gradient look like?: A line sloping downwards from left to right.
How do you find the $x$ -intercept?: Set $y=0$ and solve for $x$ .
How do you find the $y$ -intercept?: Set $x=0$ and find $y$ .
Find the equation with gradient $4$ through $(0,-3)$ .: $y=4x-3$
How do you find the equation of a line through two points?: Find $m$ , substitute one point into $y=mx+c$ , and solve for $c$ .
How do you check if a point lies on a line?: Substitute its x-value and see if you get its y-value.
What does the gradient mean in a real-life graph?: The rate of change, e.g. litres per minute.

Exam questions on Linear functions and graphs

A straight line has equation $y=-2x+6$ .
The line, the $x$ -axis and the $y$ -axis form a triangle. Find the area of this triangle.2 marks
A straight line passes through the points $A(1,3)$ and $B(5,11)$ .
Determine whether the point $C(10,20)$ lies on the line $AB$ .2 marks
A swimming pool is being filled at a constant rate. After 2 minutes it holds 150 litres of water, and after 6 minutes it holds 450 litres. The volume $V$ litres after $t$ minutes follows a linear relationship.
Find the gradient of the line and hence write down the equation for $V$ in terms of $t$ .3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).