CAIE IGCSE Additional Math 7.1 straight-line equations

Use this line-equations page to find gradients, sketch straight lines and solve intersections between two line equations.

Exam points

Find gradients of lines from coordinate pairs or diagram information accurately.
Sketch straight-line graphs such as y=5x-2 over a stated interval on axes.
Solve the intersection of a line through two points with another straight line.

[Maximum number: 5]

A straight line passes through the points (4,23) and (-8,29). Find the point of intersection, P, of this line with the line y=2x+5.

$y=-\frac12x+25\text{ isw}$
B3.

M1 for $m=\frac{29-23}{-8-4}$ oe or $-\frac12$ , and M1 FT for $\frac{y-23}{x-4}=$ their $-\frac12$ oe, or y= their $-\frac12x+c$ and $23=-\frac12\times4+c$ oe.

OR M1 for solving 23=4m+c, 29=-8m+c for $m=-\frac12$ or c=25, and M1 FT for correctly using their m or their c to find c or m.

Solves their linear equation simultaneously with y=2x+5 to find x or y. M1: FT their $y=-\frac12x+25$ oe.

(8,21). A1.

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7.1. Use straight-line equations question 1