Intercept

1.

The \(y\)-intercept is the point where the graph intersects the \(y\)-axis. Since the \(y\)-axis is also the line \(x = 0\), the \(x\)-value of this point will always be \(0\).

The \(x\)-intercept is the point where the graph intersects the \(x\)-axis. Since the \(x\)-axis is also the line \(y = 0\), the \(y\)-value of this point will always be \(0\).

To find the \(y\)-intercept, let's substitute \(x = 0\) into the equation and solve for \(y\):

\(\begin{aligned}

4 \cdot 0-3 y &=17 \\

-3 y &=17 \\

y &=-\frac{17}{3}

\end{aligned}\)

So the \(y\)-intercept is \(\left(0,-\frac{17}{3}\right)\).

To find the \(x\) intercept, let's substitute \(y = 0 \) into the equation and solve for \(x\):

\(\begin{array}{r}

4 x-3 \cdot 0=17 \\

4 x=17 \\

x=\frac{17}{4}

\end{array}\)

So the \(x\)-intercept is \(\left(\frac{17}{4}, 0\right)\).

In conclusion,

• The \(y\)-intercept is \(\left(0,-\frac{17}{3}\right)\).
• The \(x\)-intercept is \(\left(\frac{17}{4}, 0\right)\).

2.

The \(y\)-intercept is the point where the graph intersects the \(y\)-axis. Since the \(y\)-axis is also the line \(x = 0\), the \(x\)-value of this point will always be \(0\).

The \(x\)-intercept is the point where the graph intersects the \(x\)-axis. Since the \(x\)-axis is also the line \(y = 0\), the \(y\)-value of this point will always be \(0\).

To find the \(y\)-intercept, let's substitute \(x = 0\) into the equation and solve for \(y\):

\(\begin{aligned}

y-3 &=5(0-2) \\

y-3 &=-10 \\

y &=-7

\end{aligned}\)

So the \(y\)-intercept is \( (0, -7)\).

To find the \(x\) intercept, let's substitute \(y = 0 \) into the equation and solve for \(x\):

\(\begin{aligned}

0-3 &=5(x-2) \\

-3 &=5 x-10 \\

7 &=5 x \\

1.4 &=x

\end{aligned}\)

So the \(x\)-intercept is \( (1.4, 0)\).

In conclusion,

• The \(y\)-intercept is \( (0, -7)\).
• The \(x\)-intercept is \( (1.4, 0)\).

3.

The \(x\)-intercept is the point where the graph intersects the \(x\)-axis. Since the \(x\)-axis is also the line \(y = 0\), the \(y\)-value of this point will always be \(0\).

The \(y\)-intercept is the point where the graph intersects the \(y\)-axis. Since the \(y\)-axis is also the line \(x = 0\), the \(x\)-value of this point will always be \(0\).

To find the \(x\) intercept, let's substitute \(y = 0 \) into the equation and solve for \(x\):

\(\begin{aligned}

0 &=11 x+6 \\

-6 &=11 x \\

-\frac{6}{11} &=x

\end{aligned}\)

So the \(x\)-intercept is \(\left(-\frac{6}{11}, 0\right)\).

To find the \(y\)-intercept, let's substitute \(x = 0\) into the equation and solve for \(y\):

\(\begin{aligned}

&y=11 \cdot 0+6 \\

&y=6

\end{aligned}\)

So the \(y\)-intercept is \( (0, 6) \). Generally, in linear equations of the form \(y=m x+b\) (which is called slope-intercept form), the \(y\)-intercept is \(( 0, b) \).

In conclusion,

• The \(x\)-intercept is \(\left(-\frac{6}{11}, 0\right)\).
• The \(y\)-intercept is \( (0, 6) \).

4.

The \(y\)-intercept is the point where the graph intersects the \(y\)-axis. Since the \(y\)-axis is also the line \(x = 0\), the \(x\)-value of this point will always be \(0\).

The \(x\)-intercept is the point where the graph intersects the \(x\)-axis. Since the \(x\)-axis is also the line \(y = 0\), the \(y\)-value of this point will always be \(0\).

To find the \(y\)-intercept, let's substitute \(x = 0\) into the equation and solve for \(y\):

\(\begin{aligned}

-7 \cdot 0-6 y &=-15 \\

-6 y &=-15 \\

y &=\frac{15}{6} \\

y &=\frac{5}{2}

\end{aligned}\)

So the \(y\)-intercept is \(\left(0, \frac{5}{2}\right)\).

To find the \(x\) intercept, let's substitute \(y = 0 \) into the equation and solve for \(x\):

\(\begin{aligned}

-7 x-6 \cdot 0 &=-15 \\

-7 x &=-15 \\

x &=\frac{15}{7}

\end{aligned}\)

So the \(x\)-intercept is \(\left(\frac{15}{7}, 0\right)\).

In conclusion,

• The \(y\)-intercept is \(\left(0, \frac{5}{2}\right)\).
• The \(x\)-intercept is \(\left(\frac{15}{7}, 0\right)\).