Q. Find the slope of the line \(y = x + 18\).

Q: What is the slope of the line y = x + 18?

The slope is the coefficient of x, so m = 1.

Q: How do you identify slope from the slope-intercept form?

In y = mx + b, m is the slope and b is the y-intercept. For y = x + 18, m = 1.

Q: What is the y-intercept of y = x + 18?

The y-intercept is b = 18, corresponding to the point (0, 18).

Q: How would you graph the line quickly?

Plot (0,18). Use slope 1: rise 1, run 1 to get (1,19), then draw the line through those points.

Q: What slope is parallel to this line?

Any parallel line has the same slope: 1.

Q: Is this line horizontal or vertical?

Neither. horizontal line has slope 0, a vertical line has undefined slope; this line has slope 1.

Answer

The line is in slope–intercept form \(y=mx+b\); comparing \(y=x+18\) gives \(m=1\). Final result: slope = 1

find the slope of the line (y = x + 18).

Detailed Explanation

Identify the slope-intercept form. The equation of a line in slope-intercept form is\( y = mx + b \)
where \( m \) is the slope and \( b \) is the y-intercept.
Compare the given equation to the slope-intercept form. The given equation is\( y = x + 18 \).
The coefficient of \( x \) is the slope. Here the coefficient of \( x \) is 1, so

\( m = 1 \).
Check with two points on the line. Choose \( x = 0 \) to find the y-intercept:\( y = 0 + 18 = 18 \), so one point is \( (0,\,18) \).
Choose \( x = 1 \):

\( y = 1 + 18 = 19 \), so another point is \( (1,\,19) \).
Use the slope formula to verify. For points \( (x_1,y_1) = (0,\,18) \) and \( (x_2,y_2) = (1,\,19) \),\( m = \dfrac{y_2 – y_1}{x_2 – x_1} = \dfrac{19 – 18}{1 – 0} = \dfrac{1}{1} = 1 \).
Conclusion:\( m = 1 \).

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FAQs

What is the slope of the line \(y = x + 18\)?

The slope is the coefficient of \(x\), so \(m = 1\).

How do you identify slope from the slope-intercept form?

In \(y = mx + b\), \(m\) is the slope and \(b\) is the y-intercept. For \(y = x + 18\), \(m = 1\).

What is the y-intercept of \(y = x + 18\)?

The y-intercept is \(b = 18\), corresponding to the point \((0, 18)\).

How would you graph the line quickly?

Plot \((0,18)\). Use slope \(1\): rise 1, run 1 to get \((1,19)\), then draw the line through those points.

What is the slope between the points \((0,18)\) and \((1,19)\)?

Slope = \(\frac{19-18}{1-0} = 1\).

What slope is perpendicular to this line?

What slope is parallel to this line?

Any parallel line has the same slope: \(1\).

Is this line horizontal or vertical?

Neither. horizontal line has slope \(0\), a vertical line has undefined slope; this line has slope \(1\).

This line has slope one and rising.
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