a The slopes of parallel lines are the same. Therefore, to find the slope of a parallel line, we need to know the slope of the given line. Let's calculate it by substituting the points that lie on the given line into the Slope Formula.
The slope of the given line — and, consequently, of the parallel line — is - 4. We can write a partial equation of our line using the slope-intercept form.
y= mx+ b
↓
y= - 4x+ b
Next, by substituting the given point ( 4, 3) into the above equation, we can find the y-intercept b.
Now that we know that b= 19, we can write the equation of our line.
y=- 4x+ 19
b Now we want to find the equation of the perpendicular line that passes through the given point. When two lines are perpendicular, their slopes are negative reciprocals. This means that their product must be -1.
m_1* m_2=- 1
From Part A, we know that the slope of the given line is - 4. We can substitute - 4 for m_1 into the equation to find m_2, the slope of the perpendicular line.
The slope of the perpendicular line is 14. We can write the partial equation of this line by recalling the slope-intercept form.
y= mx+ b
↓
y= 1/4x+ b
Next, by substituting the given point ( 4, 3) into the equation, we can find the y-intercept b.
