Questions: Question 3 Mark this question A line contains the points (4,3) and (-3,-11). What is the slope-intercept form of the equation of this line? y=1/2 x+1 y=2 x-5 y=-2 x+11 y=-1/2 x+5

Question 3
Mark this question

A line contains the points (4,3) and (-3,-11).

What is the slope-intercept form of the equation of this line?
y=1/2 x+1
y=2 x-5
y=-2 x+11
y=-1/2 x+5

Transcript text: Question 3 Mark this question A line contains the points $(4,3)$ and $(-3,-11)$. What is the slope-intercept form of the equation of this line? $y=\frac{1}{2} x+1$ $y=2 x-5$ $y=-2 x+11$ $y=-\frac{1}{2} x+5$

Solution

Solution Steps

Step 1: Find the Slope of the Line

To find the slope $ m $ of the line passing through the points $(4,3)$ and $(-3,-11)$, we use the formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the given points:

\[ m = \frac{-11 - 3}{-3 - 4} = \frac{-14}{-7} = 2 \]

Step 2: Use the Point-Slope Form to Find the Equation

With the slope $ m = 2 $ and using one of the points, say $(4, 3)$, we can use the point-slope form of the equation of a line:

\[ y - y_1 = m(x - x_1) \]

Substituting the values:

\[ y - 3 = 2(x - 4) \]

Step 3: Convert to Slope-Intercept Form

Simplify the equation to get it into the slope-intercept form $ y = mx + b $:

\[ y - 3 = 2x - 8 \]

Add 3 to both sides: