Questions: Per the straight line defined by the points (4,59) and (6,83), determine the slope (m) and y-intercept (b). Do not round the answers. m= b=

Transcript text: Per the straight line defined by the points ( 4,59 ) and ( 6,83 ), determine the slope ( $m$ ) and $y$-intercept (b). Do not round the answers. $m=$ $\square$ $b=$ $\square$

Solution

Solution Steps

Step 1: Calculate the slope ($m$)

The slope $m$ of a straight line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substitute the given points $(4, 59)$ and $(6, 83)$: \[ m = \frac{83 - 59}{6 - 4} = \frac{24}{2} = 12 \] Thus, the slope is: \[ m = 12 \]

Step 2: Calculate the $y$-intercept ($b$)

The equation of a straight line is: \[ y = mx + b \] Substitute the slope $m = 12$ and one of the points, say $(4, 59)$, into the equation: \[ 59 = 12(4) + b \] Solve for $b$: \[ 59 = 48 + b \\ b = 59 - 48 \\ b = 11 \] Thus, the $y$-intercept is: \[ b = 11 \]