Question

Find the equation of the line with slope 1/2 and going through the point (-4,-5). Put in slope-intercept form.

Answer 1

The equation of a line passing through a point A is given as

$y-y_1=m(x-x_1)\text{ ------ equation 1}$

where

$\begin{gathered} x_{1\text{ }},y_1_{} \\ \end{gathered}$

are the coordinates of the point A

$m\text{ is the slope or gradient of the line}$

In slope-intercept form, we have

$\begin{gathered} y\text{ = mx + c ----- equation 2} \\ \text{where } \\ c\Rightarrow y-intercept\text{ of the line, obtained as the value of y when x equals zero} \end{gathered}$

Thus, when

$\begin{gathered} m\text{ = }\frac{1}{2} \\ x_1=\text{ -4} \\ y_1\text{ = -5} \end{gathered}$

Substitute the above values in equation 1

$\begin{gathered} y\text{ - (-5) = }\frac{1}{2}(x\text{ - (-4))} \\ y+5\text{ = }\frac{1}{2}(x+4) \\ \text{open the brackets} \\ y\text{ +5 = }\frac{1}{2}x\text{ + 2} \\ collect\text{ like terms,} \\ y\text{ = }\frac{1}{2}x\text{ + 2 -5} \\ \Rightarrow y\text{ = }\frac{1}{2}x\text{ -3} \\ \end{gathered}$

Hence, in slope-intercept form, the equation of the line with slope 1/2.and going through the point (-4.-5) is given as

$\begin{gathered} y\text{ =}\frac{1}{2}x\text{ + (-3)} \\ \end{gathered}$

This is in comparison with equation 2, which is the general equation of a line, in slope-intercept form.