Q. Find the y-intercept of the line \(y = \frac{8}{9}x + 2\).

Q: What is the y-intercept of y=\frac{8}{9}x+2?

The y-intercept is the constant term b=2; the point is (0,2).

Q: How do you identify slope and intercept in y=\frac{8}{9}x+2?

In slope-intercept form y=mx+b, the slope is m=\frac{8}{9} and the y-intercept is b=2.

Q: How do you find the y-intercept from standard form Ax+By=C?

Set x=0 and solve: y=\frac{C}{B} (provided B\neq0).

Q: How can you graph y=\frac{8}{9}x+2 using the y-intercept?

Plot (0,2) then use the slope: rise 8, run 9 to plot another point, and draw the line through them.

Q: How do you find the x-intercept of y=\frac{8}{9}x+2?

Set y=0: 0=\frac{8}{9}x+2 → x=-\frac{9}{4}. The x-intercept is \left(-\frac{9}{4},0\right).

Q: How do you check if a point (a,b) lies on the line?

How do you check if a point (a,b) lies on the line?

Q: What does the y-intercept represent in context?

It gives the value of y when x=0; often an initial value or starting amount in real-world problems.

Q: How do you convert y=\frac{8}{9}x+2 to standard form?

Multiply by 9: 9y=8x+18. Rearranged: -8x+9y=18 (or 8x-9y=-18).

Answer

see the next answer here to check y-intercept: set x = 0.
\(y = \frac{8}{9}\cdot 0 + 2 = 2.\)
So the y-intercept is \((0,2)\).

Detailed Explanation

Solution (step-by-step)

Recognize the form of the line.The equation is given as
\( y = \tfrac{8}{9}x + 2 \), which is in slope–intercept form \( y = mx + b \).In this form, \(m\) is the slope and \(b\) is the y‑intercept (the value of \(y\) when \(x=0\)).
Identify the y‑intercept parameter \(b\).Compare \( y = \tfrac{8}{9}x + 2 \) with \( y = mx + b \). The constant term is
\( b = 2 \).This means the y‑coordinate of the intercept is \(2\).
Verify by substituting \(x=0\).To confirm, set \( x = 0 \) and compute \(y\):
\( y = \tfrac{8}{9}\cdot 0 + 2 = 0 + 2 = 2 \).
State the y‑intercept.The y‑intercept point is
\( (0,\,2) \), and the y‑intercept value is
\(2\).

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FAQs

What is the y-intercept of \(y=\frac{8}{9}x+2\)?

The y-intercept is the constant term \(b=2\); the point is \((0,2)\).

How do you identify slope and intercept in \(y=\frac{8}{9}x+2\)?

In slope-intercept form \(y=mx+b\), the slope is \(m=\frac{8}{9}\) and the y-intercept is \(b=2\).

How do you find the y-intercept from standard form \(Ax+By=C\)?

Set \(x=0\) and solve: \(y=\frac{C}{B}\) (provided \(B\neq0\)).

How can you graph \(y=\frac{8}{9}x+2\) using the y-intercept?

Plot \((0,2)\) then use the slope: rise 8, run 9 to plot another point, and draw the line through them.

How do you find the x-intercept of \(y=\frac{8}{9}x+2\)?

Set \(y=0\): \(0=\frac{8}{9}x+2\) → \(x=-\frac{9}{4}\). The x-intercept is \(\left(-\frac{9}{4},0\right)\).

How do you check if a point \((a,b)\) lies on the line?

What does the y-intercept represent in context?

It gives the value of \(y\) when \(x=0\); often an initial value or starting amount in real-world problems.

How do you convert \(y=\frac{8}{9}x+2\) to standard form?

Multiply by 9: \(9y=8x+18\). Rearranged: \(-8x+9y=18\) (or \(8x-9y=-18\)).

Find the y-intercept: it's at (0, 2).
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