Q. how to find y-intercept in (y = mx + c)

Answer

Set \(x=0\) in \(y=mx+c\) to get \(y=c\), so the y-intercept is the point \((0,c)\) and its y-coordinate is \(c\).

Detailed Explanation

How to find the y-intercept of the line y = mx + c

Recall the definition of the y-intercept.

The y-intercept is the point where the graph of the function crosses the y-axis. Points on the y-axis have x-coordinate equal to 0.
Set x equal to 0 in the equation.

Start from the equation of the line: \( y = mx + c \).

Substitute \( x = 0 \).
Compute y after substitution.

After substitution you get: \( y = m\cdot 0 + c \).

Since \( m\cdot 0 = 0 \), this simplifies to \( y = c \).
State the y-intercept as a point.

The y-coordinate at the intercept is \( c \), and the x-coordinate is \( 0 \). Therefore the y-intercept point is \( (0,\,c) \).
Interpretation.

In the slope-intercept form \( y = mx + c \), the constant \( c \) is the y-intercept: it gives the height where the line crosses the y-axis. The parameter \( m \) is the slope and does not affect the x-coordinate of the intercept (which remains 0).

Final answer: The y-intercept of \( y = mx + c \) is \( c \), and the intercept point is \( (0,\,c) \).

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FAQs

What is the y-intercept in \displaystyle y=mx+c?

The y-intercept is c because setting x=0 in \displaystyle y=mx+c gives y=c, so the intercept point is (0,c).

How do I find the y-intercept from any linear equation?

Rearrange the equation to \displaystyle y=mx+c (slope-intercept form). Then set x=0; the resulting y value is the y-intercept.

How do I find the y-intercept graphically?

Locate where the line crosses the y-axis (where x=0). The y-coordinate of that crossing is the y-intercept; the point is (0,c).

How do I find the y-intercept if the equation is \displaystyle Ax+By=C?

Set x=0, giving By=C, so y=C/B (assuming B≠0). The y-intercept point is (0, C/B).

What if the slope is zero or undefined?

If slope m=0, line is horizontal: \displaystyle y=c and every point has y-intercept c. Vertical lines x=a are not \displaystyle y=mx+c and have no single y-intercept unless a=0 (then every y is on the line).

How does the constant c affect the graph of \displaystyle y=mx+c?

The constant c shifts the line vertically: increasing c moves the line up, decreasing c moves it down; slope m (tilt) stays the same.

How do I find the y-intercept from a table of values?

Find the row where x=0; the corresponding y is the y-intercept. If x=0 is missing but points are linear, interpolate or fit the line first.

How do I find the y-intercept for a non-linear function y=f(x)?

Set x=0 in y=f(x). The value y=f(0) is the y-intercept (point (0, f(0))). This works for any function expression.

How do I find the x-intercept from \displaystyle y=mx+c?

Set y=0 and solve 0=mx+c, giving x=-c/m provided m≠0. The x-intercept is (-c/m, 0).

Get the y-intercept from y = mx + c.
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