Question

Write the equation of the line that passes through (-3, 5) and (2, 10) in slope intercept form A) y=x+8 B) y=x-8C) y=-5x-10D)y=-5x+20

Answer 1

Step 1:

In this question, we are given the following:

Write the equation of the line that passes through (-3, 5) and (2, 10) in slope -intercept form

A) y=x+8 B) y=x-8 C) y=-5x-10 D)y=-5x+20

Step 2:

The details of the solution are as follows:

The equation of the line that passes through ( -3, 5 ) and ( 2, 10 ) is:

`\begin{gathered} y\text{ - y}_1=\text{ m \lparen x - x}_1) \\ where\text{ \lparen x}_1,\text{ y}_1)\text{ = \lparen-3, 5 \rparen and \lparen x}_2,\text{ y}_2)\text{ = \lparen 2, 10 \rparen} \\ \end{gathered}`
`\text{m = }(y_2-y_1)/(x_2-x_1)=(10-5)/(2-(-3))=(5)/(5)\text{ = 1}`
`\begin{gathered} The\text{ new equation will be:} \\ y\text{ - 5 = 1 \lparen x - - 3\rparen} \\ \text{y - 5 = 1 \lparen x + 3\rparen} \\ y\text{ - 5 = x + 3} \\ y\text{ = x + 3 + 5} \\ y\text{ = x + 8} \end{gathered}`

CONCLUSION:

The final answer is:

`y\text{ = x + 8 \lparen OPTION A\rparen}`