Q. Find the y-intercept of the line \(y = \frac{7}{9}x + \frac{2}{3}\).

Q: What is the y-intercept of the line y = \frac{7}{9}x + \frac{2}{3}?

The y-intercept is b = \frac{2}{3}, which as a point is (0,\frac{2}{3}).

Q: How do you find a y-intercept from slope-intercept form?

In y = mx + b, the constant term b is the y-intercept. Here m = \frac{7}{9} and b = \frac{2}{3}.

Q: How do you find the x-intercept of this line?

Set y=0 and solve: 0 = \frac{7}{9}x + \frac{2}{3} gives x = -\frac{6}{7}. The x-intercept is \left(-\frac{6}{7}, 0\right).

Q: How do I graph the line using slope and y-intercept?

Plot (0,\frac{2}{3}). Use slope m=\frac{7}{9}: from that point go right 9 and up 7 to get another point, then draw the line through them.

Q: What is \frac{2}{3} as a decimal?

\frac{2}{3} = 0.666\dots (repeating).

Q: How do I write the line if given slope and y-intercept?

Use y = mx + b. With slope \frac{7}{9} and y-intercept \frac{2}{3}, the equation is y = \frac{7}{9}x + \frac{2}{3}.

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

Set x = 0 and solve for y: y = \frac{C}{B}, provided B \neq 0.

Answer

Set x = 0 in \(y = \frac{7}{9}x + \frac{2}{3}\). Then \(y = \frac{2}{3}\). So the y-intercept is \((0,\frac{2}{3})\).

Detailed Explanation

Write the equation in slope–intercept form and identify the constant term. The given line is
\(y = \frac{7}{9}x + \frac{2}{3}\). In the form \(y = mx + b\), the y-intercept is the constant \(b\). Here \(b = \frac{2}{3}\).
Recall the y-intercept occurs where \(x = 0\). Substitute \(x = 0\) into the equation:
\(y = \frac{7}{9}\cdot 0 + \frac{2}{3}\).

Compute the product and sum: \(\frac{7}{9}\cdot 0 = 0\), so \(y = 0 + \frac{2}{3} = \frac{2}{3}\).
State the y-intercept as a coordinate and as a value. The y-intercept point is \((0,\tfrac{2}{3})\), and the y-intercept (the y-value) is \(\tfrac{2}{3}\) (which is equal to \(0.\overline{6}\)).

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FAQs

What is the y-intercept of the line \(y = \frac{7}{9}x + \frac{2}{3}\)?

The y-intercept is \(b = \frac{2}{3}\), which as a point is \((0,\frac{2}{3})\).

How do you find a y-intercept from slope-intercept form?

In \(y = mx + b\), the constant term \(b\) is the y-intercept. Here \(m = \frac{7}{9}\) and \(b = \frac{2}{3}\).

How do you find the x-intercept of this line?

Set \(y=0\) and solve: \(0 = \frac{7}{9}x + \frac{2}{3}\) gives \(x = -\frac{6}{7}\). The x-intercept is \(\left(-\frac{6}{7}, 0\right)\).

How do I graph the line using slope and y-intercept?

Plot \((0,\frac{2}{3})\). Use slope \(m=\frac{7}{9}\): from that point go right 9 and up 7 to get another point, then draw the line through them.

What is \(\frac{2}{3}\) as a decimal?

\(\frac{2}{3} = 0.666\dots\) (repeating).

Is the y-intercept positive or negative?

How do I write the line if given slope and y-intercept?

Use \(y = mx + b\). With slope \(\frac{7}{9}\) and y-intercept \(\frac{2}{3}\), the equation is \(y = \frac{7}{9}x + \frac{2}{3}\).

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

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

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