Question

Instructions:Select the correct answer from each drop-down menu.


The equation of the graphed line in slope-point form using the point (2, -1) is ________

a) $y+1=4x-8$
b) $y+1= \frac{1}{4}(x-2)$

and its equation in slope-intercept form is _________

a) $y= \frac{x}{4}- \frac{3}{2}$
b) $4y=x-6$

Answer 1

The equation of the graphed line in slope-point form using the point (2, -1) is
b) $y+1= \frac{1}{4}(x-2)$

and its equation in slope-intercept form is _________
a) $y= \frac{x}{4}- \frac{3}{2}$

Answer 2

Answer:

(1) $y+1=\frac{1}{4}(x-2)$

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

Step-by-step explanation:

From the given graph it is clear that the line passes through two point (-2,-2) and (2,-1). So, the slope of the line is

$Slope=\dfrac{y_2-y_1}{x_2-x_1}$

$Slope=\dfrac{-1-(-2)}{2-(-2)}$

$Slope=\dfrac{1}{4}$

Slope of the given line is 1/4.

Point slope form of a line is

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

where, m is the slope.

The slope of the line is 1/4 and it passes through the point (2,-1), So, the point slope form of the given line is

$y-(-1)=\frac{1}{4}(x-2)$

$y+1=\frac{1}{4}(x-2)$

The point slope form of the given line is $y+1=\frac{1}{4}(x-2)$.

The point slope form of a line is

$y=mx+b$

where, m is slope and b is y-intercept.

Simplify the above equation to find the slope intercept form of given line is

$y+1=\frac{1}{4}(x)+\frac{1}{4}(-2)$

$y+1=\frac{x}{4}-\frac{1}{2}$

Subtract 1 from both sides.

$y+1-1=\frac{x}{4}-\frac{1}{2}-1$

$y=\frac{x}{4}-\frac{3}{2}$

Therefore, the slope intercept form of the given line is $y=\frac{x}{4}-\frac{3}{2}$.