Question

Find the slope, x-intercept & y-intercept of the straight line 2x - 3y + 5 = 0.$\left[3Marks\right]$

Answer 1

Given straight line is 2x - 3y + 5 = 0

Comparing given line with general from of line

ax + by + c = 0

a = 2, b= -3 &c = 5

y = $\frac{-a}{b}\times -\frac{c}{a}$

Slope is $\frac{-a}{b}=\frac{-2}{-3}=\frac{2}{3}$$\left[1Mark\right]$

Given equation can also be written in intercept form

2x - 3y + 5 = 0

2x - 3y = -5

$\frac{2x}{-5}-\frac{3y}{-5}=1$

$\frac{\frac{x}{-5}}{2}+\frac{\frac{y}{5}}{3}=1$$\left[1Mark\right]$
Comparing this equation with $\frac{x}{a}+\frac{y}{b}=1$

X- intercept = $\frac{-5}{2}$

Y- intercept = $\frac{5}{3}$$\left[1Mark\right]$