Gradient-intercept form of a line?

y=mx+c, with gradient m and y-intercept c.

Gradient of ax+by+d=0?

m=-\frac ab (rearrange to y=mx+c).

Condition for two lines to be perpendicular?

m1\times m2=-1, i.e. m2=-\frac{1}{m1}

Gradient of a road that rises 150 m over 2500 m horizontally?

\frac{150}{2500}=0.06, a 6% incline.

What does the gradient mean in a linear model?

The rate of change of y per unit of x, with units.

Gradient of a horizontal line? Of a vertical line?

Horizontal: 0. Vertical: undefined.

2.1 Equation of a straight lineIB Maths: Applications and Interpretation SL: Flashcards

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Gradient formula from $(x_1,y_1)$ and $(x_2,y_2)$?

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Gradient formula from $(x_1,y_1)$ and $(x_2,y_2)$ ?: $m=\frac{y_2-y_1}{x_2-x_1}$
Gradient-intercept form of a line?: $y=mx+c$ , with gradient $m$ and $y$ -intercept $c$ .
Point-gradient form of a line?: $y-y_1=m(x-x_1)$
General form of a line?: $ax+by+d=0$
Gradient of $ax+by+d=0$ ?: $m=-\frac ab$ (rearrange to $y=mx+c$ ).
How do you find the $y$ -intercept of a line?: Set $x=0$ .
How do you find the $x$ -intercept of a line?: Set $y=0$ .
Condition for two lines to be parallel?: $m_1=m_2$
Condition for two lines to be perpendicular?: $m_1\times m_2=-1$ , i.e. $m_2=-\frac{1}{m_1}$
Gradient perpendicular to $m=-\frac34$ ?: $\frac43$
Gradient of a road that rises 150 m over 2500 m horizontally?: $\frac{150}{2500}=0.06$ , a 6% incline.
What does the gradient mean in a linear model?: The rate of change of $y$ per unit of $x$ , with units.
Gradient of a horizontal line? Of a vertical line?: Horizontal: $0$ . Vertical: undefined.

Exam questions on 2.1 Equation of a straight line

A line $L$ passes through the points $A(1, 4)$ and $B(5, 12)$ .
Find the equation of the line parallel to $L$ that passes through the point $(3, -1)$ . Give your answer in the form $ax+by+d=0$ , where $a$ , $b$ and $d$ are integers.2 marks
The line $l_1$ has equation $3x+4y-24=0$ .
Find the coordinates of the points where $l_1$ crosses the $x$ -axis and the $y$ -axis.2 marks
A mountain road climbs from a village at a height of 420 m above sea level to a viewpoint at a height of 570 m. The horizontal distance between the village and the viewpoint is 2.5 km. The road may be modelled as a straight line.
(i) Find the gradient of the road. (ii) Write your answer to (i) as a percentage and explain what it means for a driver.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).