Answer :
To find the equation of the line that passes through the points \((-1, 8)\) and \((2, 29)\), follow these steps:
1. Determine the slope (m) of the line:
The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substituting the given points \((-1, 8)\) and \((2, 29)\):
[tex]\[ m = \frac{29 - 8}{2 - (-1)} = \frac{21}{3} = 7.0 \][/tex]
2. Calculate the y-intercept (b) of the line:
The equation of the line in the slope-intercept form ( \(y = mx + b\) ) requires the y-intercept \(b\). Rearrange the slope-intercept equation to solve for \(b\):
[tex]\[ b = y - mx \][/tex]
Use one of the given points to find \(b\). Using the point \((-1, 8)\):
[tex]\[ b = 8 - (7.0 \times -1) = 8 + 7 = 15.0 \][/tex]
3. Write the equation of the line:
Substitute the slope \(m\) and the y-intercept \(b\) into the slope-intercept form:
[tex]\[ y = 7.0x + 15.0 \][/tex]
Hence, the equation of the line that passes through the points \((-1, 8)\) and \((2, 29)\) is:
[tex]\[ y = 7.0x + 15.0 \][/tex]
1. Determine the slope (m) of the line:
The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substituting the given points \((-1, 8)\) and \((2, 29)\):
[tex]\[ m = \frac{29 - 8}{2 - (-1)} = \frac{21}{3} = 7.0 \][/tex]
2. Calculate the y-intercept (b) of the line:
The equation of the line in the slope-intercept form ( \(y = mx + b\) ) requires the y-intercept \(b\). Rearrange the slope-intercept equation to solve for \(b\):
[tex]\[ b = y - mx \][/tex]
Use one of the given points to find \(b\). Using the point \((-1, 8)\):
[tex]\[ b = 8 - (7.0 \times -1) = 8 + 7 = 15.0 \][/tex]
3. Write the equation of the line:
Substitute the slope \(m\) and the y-intercept \(b\) into the slope-intercept form:
[tex]\[ y = 7.0x + 15.0 \][/tex]
Hence, the equation of the line that passes through the points \((-1, 8)\) and \((2, 29)\) is:
[tex]\[ y = 7.0x + 15.0 \][/tex]
