Question

A line with a slope of 2/3 passes through the point (-2, 3). What is the equation in point-slope form? Then graph it.

Answer 1

Solution:

A point-slope form for a line is given by the following equation:

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

where (x1,y1) is a point on the line, and m is a slope of this line. In this case, we have that:

(x1,y1)= (-2,3) and m = 2/3

so, the point-slope form for the given line would be:

$y-3_{}=\frac{2}{3}(x+2_{})$

so that, the correct answer is :

$y-3_{}=\frac{2}{3}(x+2_{})$

solving for y, this is equivalent to:

$y_{}=\frac{2}{3}(x+2_{})+3$

applying the distributive property, this is equivalent to:

$y\text{ = }\frac{2}{3}x+\frac{4}{3}+3$

or

$y\text{ = }\frac{2}{3}x+(\frac{4}{3}+3)$

this is equivalent to

$y\text{ = }\frac{2}{3}x+\frac{13}{3}\text{ = }\frac{2}{3}x\text{ + 4.33}$

that is:

$y\text{ = }\frac{2}{3}x\text{ + 4.33}$

then, the y-intercept is 4.33

and the graph of this line is: