To determine the x-intercept, y-intercept, and slope of the line $y = 4x + 3$:

1. Slope:

The slope of a line is the coefficient of $x$ in the slope-intercept form $y = mx + b$, where $m$ is the slope.
Here, $m = 4$.
Slope = 4

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2. Y-Intercept:

The $y$-intercept is the value of $y$ when $x = 0$.
Substitute $x = 0$ into $y = 4x + 3$:
$y = 4(0) + 3 = 3$
Y-Intercept = (0, 3)

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3. X-Intercept:

The $x$-intercept is the value of $x$ when $y = 0$.
Set $y = 0$ in $y = 4x + 3$:
$0 = 4x + 3$
Solve for $x$:
$4x = -3 \quad \implies \quad x = -\frac{3}{4}$
X-Intercept = $-\frac{3}{4}, 0$

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Summary:

• Slope: $4$
• Y-Intercept: $(0, 3)$
• X-Intercept: $\left( -\frac{3}{4}, 0 \right)$

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Would you like a graph or further explanation? 😊

Here are 5 related questions to deepen understanding:

1. How do you find the slope of a line from two points?
2. What is the equation of a line parallel to $y = 4x + 3$?
3. How do you find the equation of a line given its slope and a point?
4. What changes if the slope in $y = mx + b$ is negative?
5. Can a line have no x-intercept or y-intercept? Why?

Tip: To verify intercepts, always substitute the relevant variable (either $x = 0$ or $y = 0$) into the equation.