Question

What is the slope - intercept form of a line that passes through points(2,12) and (4,17) ?

Answer 1

A line pass through points (2, 11) and (4, 17);

The slope-intercept form of a line is given as;

`\begin{gathered} y=mx+c \\ \text{Where m = slope} \\ c=\text{ y-intercept} \\ \\ \text{But slope m=}(y_2-y_1)/(x_2-x_1) \\ \text{Where x}_1=2 \\ x_2=4 \\ y_1=11 \\ y_2=17 \\ m=(17-11)/(4-2)=(6)/(2) \\ m=3 \end{gathered}`

Also, for the y-intercept c;

`\begin{gathered} \text{But when x=2, y=11} \\ \text{let's use this point to get the c} \\ 11=3(2)+c \\ c=11-6 \\ c=5 \\ \end{gathered}`

Thus, the slope intercept equation of the line is;

y = 3x + 5