If the line y = mx + 1 is perpendicular to the line 2x + 3y = 6, what is the val

If the line y = mx + 1 is perpendicular to the line 2x + 3y = 6, what is the value of m?

If the line y = mx + 1 is perpendicular to the line 2x + 3y = 6, what is the value of m?

Correct Answer: 1.5

Step 1: Start with the equation of the line 2x + 3y = 6.
Step 2: Rearrange this equation to find the slope. To do this, solve for y.
Step 3: Subtract 2x from both sides: 3y = -2x + 6.
Step 4: Divide every term by 3 to isolate y: y = (-2/3)x + 2.
Step 5: Identify the slope of this line, which is -2/3.
Step 6: Remember that if two lines are perpendicular, their slopes are negative reciprocals of each other.
Step 7: The negative reciprocal of -2/3 is 3/2 (change the sign and flip the fraction).
Step 8: Therefore, the value of m in the line y = mx + 1 is 3/2.

Slope of a Line – Understanding how to find the slope from the equation of a line in standard form and how to use it to determine perpendicular slopes.
Perpendicular Lines – Knowing that the slopes of two perpendicular lines are negative reciprocals of each other.