If the line y = mx + c passes through the point (2, 3) and has a slope of 2, wha

₹0.0

Question: If the line y = mx + c passes through the point (2, 3) and has a slope of 2, what is the value of c? (2023)

Options:

Correct Answer: -1

Exam Year: 2023

Solution:

Using y = mx + c: 3 = 2(2) + c => c = -1.

If the line y = mx + c passes through the point (2, 3) and has a slope of 2, what is the value of c? (2023)

If the line y = mx + c passes through the point (2, 3) and has a slope of 2, what is the value of c? (2023)

Step 1: Identify the equation of the line, which is y = mx + c.
Step 2: Note that 'm' is the slope of the line. Here, m = 2.
Step 3: The line passes through the point (2, 3). This means when x = 2, y = 3.
Step 4: Substitute the values into the equation: y = mx + c becomes 3 = 2(2) + c.
Step 5: Calculate 2(2) which equals 4. Now the equation is 3 = 4 + c.
Step 6: To find c, rearrange the equation: c = 3 - 4.
Step 7: Calculate 3 - 4, which equals -1. Therefore, c = -1.

Linear Equations – Understanding the equation of a line in slope-intercept form (y = mx + c) and how to find the y-intercept (c) when given a point and slope.