Question

Write the equation of the line in intercept formList the x and y-intercepts:(f) through (1,3) and (-2,4)

Answer 1

• x-intercept = 10

,

• y-intercept = 10/3

Step-by-step explanation:

Given the points​:

`\begin{gathered} (x_1,y_1)=(1,3) \\ \mleft(x_2,y_2\mright)=\mleft(-2,4\mright) \end{gathered}`

First, determine the equation of the line using the two-point form:

`\begin{gathered} (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \\ (y-3)/(x-1)=(4-3)/(-2-1) \\ (y-3)/(x-1)=(1)/(-3) \\ -3(y-3)=x-1 \\ -3y+9=x-1 \\ x+3y=9+1 \\ x+3y=10 \end{gathered}`

Next, express it in the intercept form:

`\begin{gathered} (x)/(10)+(3y)/(10)=(10)/(10) \\ (x)/(10)+(y)/((10)/(3))=1 \end{gathered}`

Therefore, the intercepts are:

• x-intercept = 10

,

• y-intercept = 10/3

,

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