Question

What is the slope-intercept form equation of the line that passes through (1, 3) and (3, 7)?

y = −2x + 1

y = −2x − 1

y = 2x + 1

y = 2x − 1

Answer 1

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 1}}\quad ,&{\color{blue}{ 3}})\quad &({\color{red}{ 3}}\quad ,&{\color{blue}{ 7}})
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}
\\ \quad \\

y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\
\qquad \uparrow\\
\textit{point-slope form} \)

Answer 2

lets find the slope by using the slope formula :
slope(m) = (y2 - y1) / (x2 - x1)
(1,3)...x1 = 1 and y1 = 3
(3,7)...x2 = 3 and y2 = 7
now we sub
slope(m) = (7 - 3) / (3 - 1)
slope(m) = 4/2
slope(m) = 2

now that we know the slope, we will find the y intercept by using the formula :
y = mx + b (the m stands for the slope and the b stands for the y intercept)
slope(m) = 2
you can use either of your points ... (1,3)...x = 1 and y = 3
now we sub
3 = 2(1) + b (by the way, we are solving for b, the y intercept)
3 = 2 + b
3 - 2 = b
1 = b

so your equation is : y = 2x + 1

Answer 3

wow thank you so much. really appreciate it