graph the linethrough the given point with the indicated slope graph the line on the same set of coordinate axis ques(point is 2,3) slope are a(m=0)b(1)c(2)d(-3)

Let's go step by step to graph the lines through the point \( (2, 3) \) for the given slopes.

### Equation of the Line
The general equation of a line is given by the point-slope form:
\[
y - y_1 = m(x - x_1)
\]
where:
- \( (x_1, y_1) \) is the given point, which is \( (2, 3) \),
- \( m \) is the slope.

Let's find the equations of the lines for the given slopes.

### a) Slope \( m = 0 \)
For a slope of \( 0 \), the line is horizontal.
\[
y - 3 = 0(x - 2) \implies y = 3
\]
This is a horizontal line passing through \( y = 3 \).

### b) Slope \( m = 1 \)
For a slope of \( 1 \),
\[
y - 3 = 1(x - 2) \implies y = x + 1
\]
This is the equation of the line.

### c) Slope \( m = 2 \)
For a slope of \( 2 \),
\[
y - 3 = 2(x - 2) \implies y = 2x - 1
\]
This is the equation of the line.

### d) Slope \( m = -3 \)
For a slope of \( -3 \),
\[
y - 3 = -3(x - 2) \implies y = -3x + 9
\]
This is the equation of the line.

### Graphing these lines:
Each line passes through the point \( (2, 3) \) but has different slopes, so the angles at which they ascend or descend are different.

Would you like me to graph them for you?

graph the line through the given point with the indicated slope. graph the line on the same set of coordinate axes. (point is (2,3), slopes are: a) m=0, b) m=1, c) m=2, d) m=-3)

Learn how to graph lines through the point (2, 3) with different slopes (0, 1, 2, and -3) using the point-slope form. This problem covers key concepts in coordinate geometry and linear equations. Suitable for students in Grades 8-10.

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