Find the equation of the line that passes through the pair of points. Write your answer in slope-
intercept form.

Ask by Rojas Ball. in the United States

Mar 20,2025

Question

Find the equation of the line that passes through the pair of points. Write your answer in slope- intercept form. $$ (1,4) \cdot(2,7) $$ $$ y=\square $$

UpStudy AI · Accepted Answer

1. Find the slope $$ m $$ using the formula
   $$
   m = \frac{y_2 - y_1}{x_2 - x_1}
   $$
   Substituting the given points $$(1, 4)$$ and $$(2, 7)$$:
   $$
   m = \frac{7 - 4}{2 - 1} = \frac{3}{1} = 3
   $$

2. Use the point-slope form of the equation of a line:
   $$
   y - y_1 = m(x - x_1)
   $$
   Using the point $$(1, 4)$$ and $$ m = 3 $$:
   $$
   y - 4 = 3(x - 1)
   $$

3. Solve for $$ y $$ by expanding and isolating $$ y $$:
   $$
   y - 4 = 3x - 3
   $$
   Add $$ 4 $$ to both sides:
   $$
   y = 3x + 1
   $$

4. The equation of the line in slope-intercept form is:
   $$
   y = 3x + 1
   $$
The equation of the line is $$ y = 3x + 1 $$.

Find the equation of the line that passes through the pair of points. Write your answer in slope-
intercept form.

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