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{ = }(1)/(2) \\ x_1=\text{ -4} \\ y_1\text{ = -5} \end{gathered}`

Substitute the above values in equation 1

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{ =}(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.