# How do you write an equation in slope intercept form for the line through the given points (7,5 ); (-1, 1/5)?

##### 2 Answers

#### Explanation:

First, we need to determine the slope. The slope can be found by using the formula:

Where

Substituting the values from the points in the problem gives:

Now we can use the point-slope formula to write an equation for the line. The point-slope formula states:

Where

Substituting the slope we calculated and the first point from the problem gives:

The slope-intercept form of a linear equation is:

Where

#### Explanation:

The equation of a line in

#color(blue)"slope-intercept form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))#

where m represents the slope and b, the y-intercept.To calculate m, use the

#color(blue)"gradient formula"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))#

where# (x_1,y_1),(x_2,y_2)" are 2 coordinate points"# The 2 coordinate points are

# (7,5)" and (-1,1/5)# let

# (x_1,y_1)=(-1,1/5)" and " (x_2,y_2)=(7,5)#

#rArrm=(5-1/5)/(7+1)=(24/5)/8=3/5# We can write the partial equation as

#y=3/5x+b# To find b, substitute either of the 2 given points into the partial equation and solve for b.

#"Using " (7,5)" that is " x=7,y=5#

#rArr5=(3/5xx7)+b#

#rArrb=5-21/5=25/25-21/25=4/5#

#rArry=3/5x+4/5" is equation in slope-intercept form"#