Question

Graph a line with the same slope as the line from problem 1# (hint the one i drew the line through already)And have it go through the point (3,-4) Identify the slope:And Y-intercept:Write the point slope equation of the line (y-y1=m(x-x1) ):

Answer 1

Firstly we need to find the slope of the plotted line;

we will pick two points on the line and apply the slope formula;

$m=\frac{y_2-y_1}{x_2-x_1}$

Let's select points;

$(-9,1)\text{ and (9,7)}$

Substituting into the formula, we have;

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{7-1}{9-(-9)}=\frac{6}{9+9} \\ m=\frac{6}{18} \\ m=\frac{1}{3} \end{gathered}$

Since we have the slope and a point (3,-4) on the new line we can use the point slope formula to find the equation of the line.

$y-y_1=m(x-x_1)$

Substituting the point and the slope,we have;

$\begin{gathered} y-y_1=m(x-x_1) \\ y-(-4)=\frac{1}{3}(x-3) \\ y+4=\frac{1}{3}x-\frac{3}{3} \\ y+4=\frac{1}{3}x-1 \\ y=\frac{1}{3}x-1-4 \\ y=\frac{1}{3}x-5 \end{gathered}$

From the equation, the y intercept is the point where x = 0.

y intercept is;

$\begin{gathered} y=\frac{1}{3}x-5 \\ y=\frac{1}{3}(0)-5 \\ y=-5 \\ we\text{ have a point } \\ (0,-5) \end{gathered}$

So we have two points on the new line.

Let us proceed to locate the two points and join to produce the new line;

Above is a graph of a line parallel to the line in problem 1, with the same slope and passes through point (3,-4).

The slope intercept equation of the line is;

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

The point slope form of the equation is;

$y+4=\frac{1}{3}(x-3)$

The slope of the line is;

$m=\frac{1}{3}$

y-intercept is;

$y=-5$