Question

write an equation of the line in point - slope form that passes through the given points in the table. then write the equation in slope - intercept form
an equation of the line in point - slope form is
(simplify your answer. type an equation. type your answer in point - slope form. use integers or fractions for any numbers in the equation.)

x	y
20	185
25	215
30	245
35	275
40	305

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points, say $(x_1,y_1)=(20,185)$ and $(x_2,y_2)=(25,215)$. Then $m=\frac{215 - 185}{25 - 20}=\frac{30}{5}=6$.

Step2: Write the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(20,185)$ and $m = 6$, we get $y-185 = 6(x - 20)$.

Step3: Convert to slope - intercept form

Expand the point - slope form: $y-185=6x-120$. Then add 185 to both sides: $y=6x + 65$.

Answer:

Point - slope form: $y - 185=6(x - 20)$
Slope - intercept form: $y=6x + 65$