Math Problem Statement

Solve this

What is the value of y at the point where the line crosses the y-axis? The equation of the line is y + 5 = 6x + 13.

Solution

The equation of the line provided is:

y+5=6x+13y + 5 = 6x + 13

We need to determine the value of yy at the point where the line crosses the yy-axis. At the yy-axis, the value of xx is always 0.

Step 1: Substitute x=0x = 0 into the equation

y+5=6(0)+13y + 5 = 6(0) + 13 y+5=13y + 5 = 13

Step 2: Solve for yy

y=135y = 13 - 5 y=8y = 8

Thus, the value of yy when the line crosses the yy-axis is 8.

Would you like more details or further explanations?

Here are five related questions:

  1. How do you find the slope of the line from this equation?
  2. What is the general form of a linear equation?
  3. How do you find the xx-intercept of the line?
  4. Can you express the equation in slope-intercept form y=mx+by = mx + b?
  5. What does the slope of the line represent in this context?

Tip: When a line crosses the yy-axis, xx is always 0, which makes finding the yy-intercept straightforward.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

y + 5 = 6x + 13
y-intercept formula: Set x = 0

Theorems

To find the y-intercept, set x = 0 in the equation of a line.

Suitable Grade Level

Grades 8-10