# How do you write the equation in point slope form given (-1,4) parallel to y=-5x+2?

##### 2 Answers

#### Explanation:

The equation of a line in

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

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

where m represents the slope and# (x_1,y_1)" a point on the line"#

#"We have to know the following fact"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(" parallel lines have equal slopes")color(white)(2/2)|)))#

#y=-5x+2" is in slope-intercept form"#

#"that is " y=mx+b" where m is slope"#

#rArr" required slope " =m=-5#

#"using " m=-5" and " (x_1,y_1)=(-1,4)" then"#

#y-4=-5(x-(-1))#

#rArry-4=-5(x+1)larrcolor(red)" in point-slope form"#

See the entire solution process below:

#### Explanation:

The equation given in the problem is in slope intercept form. The slope-intercept form of a linear equation is:

Where

Therefore the slope of this line is

Because the line we are looking for is parallel to this line, by definition, it will have the same slope.

The point-slope formula states:

Where

We can substitute the slope of the first line and the values from the point in the first problem to write the equation of the line in point-slope form: