Question

Which of the following shows the graph of a line with a slope of 6/5 and a y intercept of -3?

Answer 1

Answer:

The correct option is 1.

Step-by-step explanation:

It is given that the slope of the line is 6/5 and y intercept is -3. It means the line must be passes through the point (0,-3).

The slope intercept form of a line is

$y=mx+b$

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

Substitute m=6/5 and b=-3 in the above equation to find the equation of line.

$y=\frac{6}{5}x+(-3)$

So, the equation of line is $y=\frac{6}{5}x+(-3)$.

Substitute y=0 in the above equation to find the x-intercept of the line.

$0=\frac{6}{5}x-3$

Add 3 on both the sides.

$0+3=\frac{6}{5}x-3+3$

$3=\frac{6}{5}x$

Multiply both sides by 5.

$15=6x$

Divide both sides by 6.

$\frac{15}{6}=x$

$2.5=x$

The x-intercept of the line is 2.5. It means the line must be passes through the point (2.5,0).

Since only in graph 1, the line passes through the points (0,-3) and (2.5,0), therefore the graph 1 represents the required line and option 1 is correct.