일차함수의 기울기와 특정 점을 지날 때의 미지수 값 구하기

문제

일차함수 $y = ax-3$에 대하여, $x$ 값이 1에서 3까지 증가할 때 $y$ 값은 2만큼 증가한다. 이 일차함수의 그래프가 점 $(k, -1)$을 지날 때, $k$의 값을 구하시오.

<!-- Axes -->
<line x1="-0.5" y1="0" x2="4.5" y2="0" class="primary-stroke"/> <!-- X-axis -->
<line x1="0" y1="-3.5" x2="0" y2="1.5" class="primary-stroke"/> <!-- Y-axis -->

<!-- Origin O label -->
<text x="0" y="0" class="label-text" transform="scale(1, -1) translate(-10, -15)">O</text>

<!-- X-axis ticks and labels -->
<line x1="1" y1="0" x2="1" y2="-0.1" class="primary-stroke"/>
<text x="1" y="0" class="label-text" transform="scale(1, -1) translate(0, -15)">1</text>
<line x1="2" y1="0" x2="2" y2="-0.1" class="primary-stroke"/>
<text x="2" y="0" class="label-text" transform="scale(1, -1) translate(0, -15)">2</text>
<line x1="3" y1="0" x2="3" y2="-0.1" class="primary-stroke"/>
<text x="3" y="0" class="label-text" transform="scale(1, -1) translate(0, -15)">3</text>
<line x1="4" y1="0" x2="4" y2="-0.1" class="primary-stroke"/>
<text x="4" y="0" class="label-text" transform="scale(1, -1) translate(0, -15)">4</text>
<text x="4.5" y="0" class="axis-label" transform="scale(1, -1) translate(10, -15)">x</text>

<!-- Y-axis ticks and labels -->
<line x1="0" y1="-1" x2="0.1" y2="-1" class="primary-stroke"/>
<text x="0" y="-1" class="label-text" transform="scale(1, -1) translate(-15, 0)">-1</text>
<line x1="0" y1="-2" x2="0.1" y2="-2" class="primary-stroke"/>
<text x="0" y="-2" class="label-text" transform="scale(1, -1) translate(-15, 0)">-2</text>
<line x1="0" y1="-3" x2="0.1" y2="-3" class="primary-stroke"/>
<text x="0" y="-3" class="label-text" transform="scale(1, -1) translate(-15, 0)">-3</text>
<text x="0" y="1.5" class="axis-label" transform="scale(1, -1) translate(-15, 10)">y</text>

<!-- The Line: y = x - 3 -->
<line x1="0" y1="-3" x2="4" y2="1" class="secondary-stroke" />
<text x="4.5" y="1" class="line-label" transform="scale(1, -1) translate(15, 15)">y = x - 3</text>

<!-- Points and their labels -->
<!-- Point A (1, -2) -->
<circle cx="1" cy="-2" r="0.1" class="secondary-fill" />
<text x="1" y="-2" class="point-label" transform="scale(1, -1) translate(-20, -15)">A(1, -2)</text>

<!-- Point B (3, 0) -->
<circle cx="3" cy="0" r="0.1" class="secondary-fill" />
<text x="3" y="0" class="point-label" transform="scale(1, -1) translate(5, 15)">B(3, 0)</text>

<!-- Slope visualization (dashed lines) -->
<path d="M 1 -2 L 3 -2 L 3 0" class="primary-stroke" stroke-dasharray="4 4" fill="none"/>
<text x="2" y="-2" class="label-text" transform="scale(1, -1) translate(0, -20)">Δx = 2</text>
<text x="3" y="-1" class="label-text" transform="scale(1, -1) translate(20, 0)">Δy = 2</text>

<!-- Point P (k, -1) which is (2, -1) -->
<circle cx="2" cy="-1" r="0.1" class="secondary-fill" />
<text x="2" y="-1" class="point-label" transform="scale(1, -1) translate(5, 15)">P(k, -1)</text>